The present invention relates to a state estimating apparatus for estimating the state of a system on the basis of recorded input/output data for the system.
A state estimating apparatus of this type, designed to estimate the state of a system on the basis of recorded input/output data for the system, uses the following methods.
In the first method, linearity as represented by equation (1) is assumed between a plurality of input variables (x1, x2, x3, . . . , xn) and an output variable y as a target for the input variables. The coefficients (a1, a2, a3, . . . , an) of the respective input variables are determined by the least squares method such that the estimation error is minimized, thereby determining the output variable y. EQU y=a1*x1+a2*x2+a3*x3+. . . +an*xn (1)
The second method is a method called GMDH (group method of data handling).
In the first method, non-linear relationship between input and output variables is assumed. In contrast to this, in the second method, since an object to be treated is complicated, nonlinearity is assumed between input and output variables. That is, a mathematical model handled in the second method is expressed by a higher order polynomial such as equation (2): ##EQU1##
In the second method, in order to obtain an output variable y, the coefficients (ai, aij, aijk, . . . ) of the respective input variables are obtained. In addition, the orders (n1, n2, n3, . . . ) of the respective input variables are determined. Such parameters, e.g., coefficients and orders, of the respective input variables are selected and combined on the basis of predetermined criteria for evaluation. Note that these selecting and combining operations are performed in a trial-and-error manner.
In the third method, state estimation is performed by forming a fuzzy model. According to the third method, the relationship between input and output variables is expressed by IF-THEN rules as indicated in Table 1, and state estimation is performed on the basis of this rule.
TABLE 1 ______________________________________ Rule 1: IF x1 = big, x2 = small, . . . , xn = medium THEN y = small Rule 2: IF x1 = big, x2 = small, . . . , xn = small THEN y = medium . . . Rule m: IF x1 = small, x2 = big, . . . , xn = small THEN y = big ______________________________________
These IF-THEN rules are based on either the knowledge and subjectivity of men or historical data. According to this rule, by providing membership functions as shown in FIGS. 23A and 23B for the respective input and output variables, fuzzy events can also be treated. These rules as qualitative descriptions and membership functions as quantitative descriptions correspond to parameters such as coefficients and orders obtained in the first and second methods.
The fourth method is a method of performing state estimation by using a neural network.
As shown in FIG. 24, a model of this neural network is generally constituted by a large number of nonlinear operators called neurons coupled to each other to form a network. In this case, the relationship between input and output variables of the neural network is determined by learning. That is, the relationship between input and output variables is obtained as the coupling weight of each neuron in the network by learning, thus forming a model between the input and output variables. In this case, the parameters of the model are determined by determining the structure and coupling weight of each neuron.
In the conventional first to fourth methods, since the state of a system is estimated by using mathematical expressions, a rule model, and the like, the following problems are posed.
In the first method, many types of input variables are treated, and hence many parameters of the input variables must be determined, resulting in various difficulties in forming an optimal model.
In addition, since a system exhibits a complicated state, state estimation cannot be performed by only a single model based on the above-mentioned linear expression (1). In practice, therefore, a model based on each linear expression or a model based on a complicated nonlinear expression such as equation (2) is required, and parameters are increased in number, resulting in more difficulty in handling models.
Since a system always changes, changes in the system must be reflected on a model by a learning function. In this case, it is necessary to easily modify the model. However, a model formed by converting data into parameters and rule data as in the conventional methods cannot be easily modified. Consequently, it is difficult to operate the system on-line.
Furthermore, a problem is posed in terms of handling of qualitative information of a model with respect to a new input state under insufficient data used for modeling, i.e., the reliability of the model. This is the most important point in the use of a model.
As described above, various problems are posed in the conventional methods. These problems are based on the fact that each method is designed to express the global state of a system by a standard model obtained by converting the state into several parameters.
A case-based inference apparatus is also available, which performs inference by directly using case data containing the mechanism of an input/output relationship without forming a standard model. Such an inference apparatus has an excellent local description, and hence has an excellent property of separating events from each other. Therefore, the apparatus is suitable for a description of a nonlinear phenomenon. In addition, since cases used for interference can be provided, the qualitative information of a model that is the relationship between new situation and the recorded cases in the case-base can be easily handled.
In the conventional case-based inference apparatus, the following methods and schemes are not generalized: 1 a method of retrieving case data, 2 a recording scheme of case data, 3 determination on the similarity between case data, 4 determination on the importance of case data, and 5 a method of correcting case data. Therefore, schemes depending on an object must be determined, and it is difficult to actually describe the state of a system on the basis of input/output data.